On the anisotropy theorem of Papadakis and Petrotou

Papadakis and Petrotou showed that the anisotropy of a quadratic form implies the Hard Lefschetz theorem for simplicial homology spheres in characteristic 2. These spheres are a special case of the broader family of pseudo-manifolds. In this talk, I will explain how we define a mixed volume on pseudo-manifolds using an integration map, which is linear over a connected sum decomposition. Using this decomposition, we explicitly describe the quadratic form and prove an additional combinatorial conjecture of Papadakis and Petrotou, which turns out to imply all characteristic 2 anisotropy results for pseudo-manifolds and spheres. This is joint work with Kalle Karu.

Time: 4:15-5:15pm

Location: MATH 126

Seminar Website: https://yifeng-huang-math.github.io/seminar_ubc_ag_23w.html